Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

The value of screening in siblings of patients with abdominal aortic aneurysm

Objectives. This study aimed to determine the incidence of abdominal aortic aneurysm (AAA) in a large group of siblings of Australian AAA patients to determine if screening in this group is justified. Methods. 1254 siblings of 400 index AAA patients were identified and offered aortic ultrasound screening. An age and sex matched control group was recruited from patients having abdominal CT scans for non-vascular indications. AAA was defined by an infrarenal aortic diameter of greater than or equal to3 cm or a ratio of the infrarenal to suprarenal aortic diameter of greater than or equal to2.0. A ratio of 1.0-1.5 was considered normal, and a ratio of >1.5 to

Linkage and Association Analysis of Radiation Damage Repair Genes XRCC3 and XRCC5 with Nevus Density in Adolescent Twins

Previous studies have shown that a deficiency in DNA damage repair is associated with increased cancer risk, and exposure to UV radiation is a major risk factor for the development of malignant melanoma. High density of common nevi (moles) is a major risk factor for cutaneous melanoma. A nevus may result from a mutation in a single UV-exposed melanocyte which failed to repair DNA damage in one or more critical genes. XRCC3 and XRCC5 may have an effect on nevus count through their function as components of DNA repair processes that may be involved directly or indirectly in the repair of DNA damage due to UV radiation. This study aims to test the hypothesis that the frequency of flat or raised moles is associated with polymorphism at or near these DNA repair genes, and that certain alleles are associated with less efficient DNA repair, and greater nevus density. Twins were recruited from schools in south eastern Queensland and were examined close to their 12th birthday. Nurses examined each individual and counted all moles on the entire body surface. A 10cM genome scan of 274 families (642 individuals) was performed and microsatellite polymorphisms in XRCC3 and adjacent to XRCC5 were also typed. Linkage and association of nevus count to these loci were tested simultaneously using a structural-equation modeling approach implemented in MX. There is weak evidence for linkage of XRCC5 to a QTL influencing raised mole count, and also weak association. There is also weak evidence for association between flat mole count and XRCC3. No tests were significant after correction for testing multiple alleles, nor were any of the tests for total association significant. If variation in XRCC3 or XRCC5 influences UV sensitivity, and indirectly affects nevus density, then the effects are small.

ADH genotype does not modify the effects of alcohol on high-density lipoprotein

Background: Alcohol consumption has beneficial effects on mortality which are mainly due to reduction in cardiovascular disease. These are believed to be due, at least in part, to the increase in plasma high-density lipoprotein (HDL) which is associated with alcohol consumption. It has been proposed that ADH3 genotype modifies the relationships between alcohol intake and cardiovascular disease by altering the HDL response to alcohol. The aim of this paper was to test for effects of ADH2 and ADH3 genotypes on the response of HDL components to habitual alcohol consumption. Methods: Adult male and female subjects were genotyped for ADH2 and ADH3; and plasma HDL cholesterol, apolipoprotein A-I, and apolipoprotein A-II were measured. Nine hundred one subjects had both ADH2 and ADH3 genotypes and HDL cholesterol results, while 753 had both genotypes and all three lipid results. The effect of alcohol intake on the three measured HDL components, and a factor score derived from them, was estimated for each of the ADH2 and ADH3 genotype groups. Results: All the measured components of HDL increased with increasing alcohol consumption over the range of intakes studied, 0-4 drinks per day. There were no significant interactions between alcohol consumption and ADH2 or ADH3 genotypes. Conclusions: The concept that alcohol dehydrogenase genotype and alcohol metabolic rate modify the effects of alcohol on plasma HDL concentration is not supported by our results.

The value of idiosyncratic markers and changes to conserved tRNA sequences from the mitochondrial genome of hard ticks (Acari: Ixodida: Ixodidae) for phylogenetic inference

Idiosyncratic markers are features of genes and genomes that are so unusual that it is unlikely that they evolved more than once in a lineage of organisms. Here we explore further the potential of idiosyncratic markers and changes to typically conserved tRNA sequences for phylogenetic inference. Hard ticks were chosen as the model group because their phylogeny has been studied extensively. Fifty-eight candidate markers from hard ticks ( family Ixodidae) and 22 markers from the subfamily Rhipicephalinae sensu lato were mapped onto phylogenies of these groups. Two of the most interesting markers, features of the secondary structure of two different tRNAs, gave strong support to the hypothesis that species of the Prostriata ( Ixodes spp.) are monophyletic. Previous analyses of genes and morphology did not strongly support this relationship, instead suggesting that the Prostriata is paraphyletic with respect to the Metastriata ( the rest of the hard ticks). Parallel or convergent evolution was not found in the arrangements of mitochondrial genes in ticks nor were there any reversals to the ancestral arthropod character state. Many of the markers identified were phylogenetically informative, whereas others should be informative with study of additional taxa. Idiosyncratic markers and changes to typically conserved nucleotides in tRNAs that are phylogenetically informative were common in this data set, and thus these types of markers might be found in other organisms.

The paternity of the price-quality 'value map'

In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer 'value maps'. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the 'quality' axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.

Effects of combined low-density lipoprotein apheresis and aggressive statin therapy on coronary calcified plaque as measured by computed tomography

Eight patients with heterozygous familial hypercholesterolemia who received combined long-term low-density lipoprotein apheresis and high-dose statin therapy showed a significant decrease in volume of coronary calcium over a period of 29 months as measured by, computed tomography. This suggests that the effects of aggressive lipid-lowering therapy can be assessed non-invasively and may be used as surrogate end points when testing new therapies.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Gender differences in CF phenotype associated with low bone mineral density

Adolescents and adults with CF have lower bone mineral density (BMD) than normal, but its relationship with phenotype is not well understood. Point FEV1% predicted (FEV) and rate of change of FEV are biased estimates of disease severity, because progressively older subjects represent a selected survivor population, with females at greater risk of death than males. To investigate the relationship between BMD and phenotype we used an index (predicted age at death) derived from Bayesian estimates of slope and intercept of FEV, age at last measurement and survival status. Predictive equations for the index were derived from 97 subjects (78 survivors) from the RCH CF clinic, and applied to a group of 102 comparable subjects who had BMD measured, classified as having‘mild’ ()75th), ‘moderate’ (25– 75th), or ‘severe’ (-25th centile) phenotype. Total body (TB) and lumbar spine (LS) BMD z-scores (Z) were compared, adjustingfor gender effects, using 2-way ANOVA. Annual mean change in FEV segregated, as expected, according to phenotype, ‘severe’ (ns25), ‘moderate’ (ns51) and ‘mild’ (ns25) y3.01(y3.73 to y2.30)%, y0.85(y1.36 to y0.35)%, 2.70(1.92 to 3.46)%, respectively, with no gender difference. LS and TB BMDZ were different in each phenotype (P-s 0.002), LS BMDZ for ‘severe’, ‘moderate’ and ‘mild’ y1.63(CI: y2.07 to y 1.19), y0.86(CI: y1.17 to y0.55), y0.06(CI: y0.54 to 0.41). Males had lower LS BMDZ than females overall (y1.22 (CI: y1.54 to y0.91) vs. y0.48(CI: y 0.84 to y0.12) Ps0.002). In the ‘severe’ group, males had lower TB BMDZ and LS BMDZ (PF0.002). Low BMD is associated with ‘moderate’ and ‘severe’ phenotypes, with relative preservation in females in the ‘severe’ group. Female biology (reproductive fitness) might promote resistance to bone resorption at a critical level of BMD loss.

Effects of heat treatment on the nutritional value of raw soybean selected for low trypsin inhibitor activity

1. Two broiler experiments and a layer experiments were conducted on Kunitz trypsin inhibitor (Kti) soybeans (SB) of low trypsin inhibitor (TI) activity to determine their nutritive value when included as mash in least-cost poultry diets. 2. Experiment 1 compared chick performance on the Kti or raw SB using a commercial full-fat SB meal (FFSBM) and a solvent extracted SB meal (SBM) as controls during a 20 d experimental period. Broiler experiment 2 compared Kti and raw SB, non-steamed, or steam-pelleted with and without DL-methionine supplementation added to every treatment containing 170 g SB/kg. For each broiler experiment the levels of each SB were 70, 120 and 170 g/kg with the control birds fed only 170 g SB/kg. 3. The layer experiment, compared steam-pelleted Kti and raw SB against a non-steamed Kti and raw SB each fed at two levels (70 and 110 g/kg) x 30 replicates from 29 weeks of age for 19 weeks in a completely randomised design. Production parameters were measured when diets were formulated to contain minimum required specifications and calculated apparent metabolisable energy (AME). At the completion of each trial, 2 broiler birds from each cage and 5 layer birds per treatment were killed, weighed, and their liver and pancreas weighed. 4. Both broiler experiments indicated that production parameters on the Kti SB treatments were significantly lower (P < 0.05) than on the two commercial control SB treatments. However, the Kti treatments were superior to the raw SB treatments. 5. Pancreas weight increased with increasing inclusion of both raw and Kti SB, suggesting that a TI was causing the depression in performance. The AME of the Kti SB was similar to that of commercial FFSB meal. After steam conditioning, the raw SB meal AME value of 9.5 MJ/kg dry matter (DM) was improved to 14.1 MJ/kg DM by reduced TI activity, but this AME improvement with TI activity reduction, plus the supplementation with DL-methionine on birds fed the raw SB had no effect (P > 0.05) on any parameter evaluated in experiment 2. 6. The layer experiment showed that hens on the Kti SB treatments had significantly greater live weight gain (LWG), egg weight and daily egg mass than birds given raw SB. A reduced food intake (FI) was observed in the Kti treatments but egg mass was generally similar to that on the FFSB control diet, indicating that Kti SB supported excellent egg production at an inclusion of 110 g/kg. The depressed performance observed for broiler chicks suggest that younger birds are more susceptible to the effects of SB TI.

Selective entrainment of sediment graded by size and density under waves

The influence of near-bed sorting processes on heavy mineral content in suspension is discussed. Sediment concentrations above a rippled bed of mixed quartz and heavy mineral sand were measured under regular nonbreaking waves in the laboratory. Using the traditional gradient diffusion process, settling velocity would be expected to strongly affect sediment distribution. This was not observed during present trials. In fact, the vertical gradients of time-averaged suspension concentrations were found to be similar for the light and heavy minerals, despite their different settling velocities. This behavior implies a convective rather than diffusive distribution mechanism. Between the nonmoving bed and the lowest suspension sampling point, fight and heavy mineral concentration differs by two orders of magnitude. This discrimination against the heavy minerals in the pickup process is due largely to selective entrainment at the ripple face. Bed-form dynamics and the nature of quartz suspension profiles are found to be little affected by the trialed proportion of overall heavy minerals in the bed (3.8-22.1%).

Sex- and race-related differences in cross-sectional geometry and bone density of the femoral mid-shaft in older adults

Background : Femoral shaft fracture incidence increases in older adults and is associated with low-energy trauma. Apart from bone density, the distribution and size of bone contributes to its strength. Aim : To examine if bone geometry and density of the femoral mid-shaft in older adults differs by sex and race, we studied 197 White women, 225 Black women, 242 White men, and 148 Black men aged 70-79 years participating in the Health, Aging, and Body Composition study; a prospective cohort study in the USA. A secondary purpose of the study was to examine the association of site-specific muscle and fat to bone geometry and density. Subjects and methods : Subjects were community-dwelling and reported no difficulty walking one-quarter of a mile or climbing stairs. Mid-femoral volumetric bone mineral density (vBMD, mg cm -3 ), total area (TA), cortical area (CA), medullary area (MA), cross-sectional moments of inertia (CSMI: I x , I y , J ), and muscle and fat areas (cm 2 ) were determined by computed tomography (CT; GE CT-9800, 10 mm slice thickness). Results : vBMD was greater in men than women with no difference by race ( p < 0.001). Bone areas and area moments of inertia were also greater in men than women ( p < 0.001), with Black women having higher values than White women for TA and CA. Standardizing geometric parameters for body size differences by dividing by powers of femur length did not negate the sex difference for TA and MA. Significant differences ( p < 0.05) among the four groups also remained for I x and J . Mid-thigh muscle area was an independent contributor to TA in all groups (Std beta = 0.181-0.351, p < 0.05) as well as CA in women (Std beta = 0.246-0.254, p < 0.01) and CSMI in White women (Std beta = 0.175-0.185, p < 0.05). Further, muscle area was a significant contributor to vBMD in Black women. Conclusion : These results indicate that bone geometry and density of the femoral diaphysis differs primarily by sex, rather than race, in older well-functioning adults. In addition, site-specific muscle area appears to have a potential contributory role to bone geometry parameters, especially in women.

Adsorption of supercritical fluids in non-porous and porous carbons: analysis of adsorbed phase volume and density

In this paper, we revisit the surface mass excess in adsorption studies and investigate the role of the volume of the adsorbed phase and its density in the analysis of supercritical gas adsorption in non-porous as well as microporous solids. For many supercritical fluids tested (krypton, argon, nitrogen, methane) on many different carbonaceous solids, it is found that the volume of the adsorbed phase is confined mostly to a geometrical volume having a thickness of up to a few molecular diameters. At high pressure the adsorbed phase density is also found to be very close to but never equal or greater than the liquid phase density. (C) 2003 Elsevier Science Ltd. All rights reserved.

Wall mediated transport in confined spaces: Exact theory for low density

We present a theory for the transport of molecules adsorbed in slit and cylindrical nanopores at low density, considering the axial momentum gain of molecules oscillating between diffuse wall reflections. Good agreement with molecular dynamics simulations is obtained over a wide range of pore sizes, including the regime of single-file diffusion where fluid-fluid interactions are shown to have a negligible effect on the collective transport coefficient. We show that dispersive fluid-wall interactions considerably attenuate transport compared to classical hard sphere theory.